Table of contents

r.random.surface generates a spatially dependent random surface.
The random surface is composed of values representing the deviation from the
mean of the initial random values driving the algorithm. The initial random
values are independent Gaussian random deviates with a mean of 0 and
standard deviation of 1. The initial values are spread over each output map
using filter(s) of diameter distance. The influence of each random value on
nearby cells is determined by a distance decay function based on exponent.
If multiple filters are passed over the output maps, each filter is given a
weight based on the weight inputs. The resulting random surface can have
any mean and variance, but the theoretical mean of an infinitely
large map is 0.0 and a variance of 1.0. Description of the algorithm is in
the NOTES section.

The random surface generated are composed of floating point numbers, and
saved in the category description files of the output map(s). Cell values
are uniformly or normally distributed between 1 and high values inclusive
(determined by whether the -u flag is used). The category names
indicate the average floating point value and the range of floating point
values that each cell value represents.

r.random.surface's original goal is to generate random fields for
spatial error modeling. A procedure to use r.random.surface in
spatial error modeling is given in the NOTES section.

Random surface(s). The cell values are a random distribution
between the low and high values inclusive. The category values of the
output map(s) are in the form #.# #.# to #.# where each #.#
is a floating point number. The first number is the average of the
random values the cell value represents. The other two numbers are the
range of random values for that cell value. The average mean
value of generated output map(s) is 0. The average
variance of map(s) generated is 1. The random values represent the
standard deviation from the mean of that random surface.

distance

Distance determines the spatial dependence of the output
map(s). The distance value indicates the minimum distance at which two
map cells have no relationship to each other. A distance value of 0.0
indicates that there is no spatial dependence (i.e., adjacent cell
values have no relationship to each other). As the distance value
increases, adjacent cell values will have values closer to each
other. But the range and distribution of cell values over the output
map(s) will remain the same. Visually, the clumps of lower and higher
values gets larger as distance increases. If multiple values are
given, each output map will have multiple filters, one for each set of
distance, exponent, and weight values.

exponent

Exponent determines the distance decay exponent for a particular
filter. The exponent value(s) have the property of determining
the texture of the random surface. Texture will decrease as
the exponent value(s) get closer to 1.0. Normally, exponent will be
1.0 or less. If there are no exponent values given, each filter will
be given an exponent value of 1.0. If there is at least one exponent
value given, there must be one exponent value for each distance value.

flat

Flat determines the distance at which the filter.

weight

Weight determines the relative importance of each filter. For
example, if there were two filters driving the algorithm and
weight=1.0, 2.0 was given in the command line: The second filter would
be twice as important as the first filter. If no weight values are
given, each filter will be just as important as the other filters
defining the random field. If weight values exist, there must be a
weight value for each filter of the random field.

high

Specifies the high end of the range of cell values in the output
map(s). Specifying a very large high value will minimize
the errors caused by the random surface's discretization. The
word errors is in quotes because errors in discretization are often
going to cancel each other out and the spatial statistics are far more
sensitive to the initial independent random deviates than any
potential discretization errors.

seed

Specifies the random seed(s), one for each map,
that r.random.surface will use to generate the initial set of
random values that the resulting map is based on. If the random seed
is not given, r.random.surface will get a seed from the
process ID number.

While most literature uses the term random field instead of random surface,
this algorithm always generates a surface. Thus, its use of random surface.

r.random.surface builds the random surface using a filter algorithm
smoothing a map of independent random deviates. The size of the filter is
determined by the largest distance of spatial dependence. The shape of the
filter is determined by the distance decay exponent(s), and the various
weights if different sets of spatial parameters are used. The map of
independent random deviates will be as large as the current region PLUS the
extent of the filter. This will eliminate edge effects caused by the
reduction of degrees of freedom. The map of independent random deviates will
ignore the current mask for the same reason.

One of the most important uses for r.random.surface is to determine
how the error inherent in raster maps might effect the analyses done with
those maps.

As part of my dissertation, I put together several programs that help
GRASS (4.1 and beyond) develop uncertainty models of spatial data. I hope
you find it useful and dependable. The following papers might clarify their
use: